32 research outputs found
Stochastic Coagulation and the Timescale for Runaway Growth
We study the stochastic coagulation equation using simplified models and
efficient Monte Carlo simulations. It is known that (i) runaway growth occurs
if the two-body coalescence kernel rises faster than linearly in the mass of
the heavier particle; and (ii) for such kernels, runaway is instantaneous in
the limit that the number of particles tends to infinity at fixed collision
time per particle. Superlinear kernels arise in astrophysical systems where
gravitational focusing is important, such as the coalescence of planetesimals
to form planets or of stars to form supermassive black holes. We find that the
time required for runaway decreases as a power of the logarithm of the the
initial number of particles. Astrophysical implications are briefly discussed.Comment: 16 pages, 4 figures, 1 appendi
On the thermal conduction in tangled magnetic fields in clusters of galaxies
Thermal conduction in tangled magnetic fields is reduced because heat
conducting electrons must travel along the field lines longer distances between
hot and cold regions of space than if there were no fields. We consider the
case when the tangled magnetic field has a weak homogeneous component. We
examine two simple models for temperature in clusters of galaxies: a
time-independent model and a time-dependent one. We find that the actual value
of the effective thermal conductivity in tangled magnetic fields depends on how
it is defined for a particular astrophysical problem. Our final conclusion is
that the heat conduction never totally suppressed but is usually important in
the central regions of galaxy clusters, and therefore, it should not be
neglected.Comment: 16 pages, 4 figure
Magnetic dynamo action in random flows with zero and finite correlation times
Hydromagnetic dynamo theory provides the prevailing theoretical description
for the origin of magnetic fields in the universe. Here we consider the problem
of kinematic, small-scale dynamo action driven by a random, incompressible,
non-helical, homogeneous and isotropic flow. In the Kazantsev dynamo model the
statistics of the driving flow are assumed to be instantaneously correlated in
time. Here we compare the results of the model with the dynamo properties of a
simulated flow that has equivalent spatial characteristics as the Kazantsev
flow but different temporal statistics. In particular, the simulated flow is a
solution of the forced Navier-Stokes equations and hence has a finite
correlation time. We find that the Kazantsev model typically predicts a larger
magnetic growth rate and a magnetic spectrum that peaks at smaller scales.
However, we show that by filtering the diffusivity spectrum at small scales it
is possible to bring the growth rates into agreement and simultaneously align
the magnetic spectra
Onset of Fast Magnetic Reconnection in Partially Ionized Gases
We consider quasi-stationary two-dimensional magnetic reconnection in a
partially ionized incompressible plasma. We find that when the plasma is weakly
ionized and the collisions between the ions and the neutral particles are
significant, the transition to fast collisionless reconnection due to the Hall
effect in the generalized Ohm's law is expected to occur at much lower values
of the Lundquist number, as compared to a fully ionized plasma case. We
estimate that these conditions for fast reconnection are satisfied in molecular
clouds and in protostellar disks.Comment: 19 pages, 1 figure, 1 tabl
Model of two-fluid reconnection
A theoretical model of quasi-stationary, two-dimensional magnetic
reconnection is presented in the framework of incompressible two-fluid
magnetohydrodynamics (MHD). The results are compared with recent numerical
simulations and experiment.Comment: 4 pages, 1 figure, accepted to Physical Review Letter
Magnetic dynamo action in astrophysical turbulence
We investigate the structure of magnetic field amplified by turbulent
velocity fluctuations, in the framework of the kinematic Kazantsev-Kraichnan
model. We consider Kolmogorov distribution of velocity fluctuations, and assume
that both Reynolds number and magnetic Reynolds number are very large. We
present the full numerical solution of the model for the spectra and the growth
rates of magnetic fluctuations. We consider astrophysically relevant limits of
large and small magnetic Prandtl numbers, and address both helical and
nonhelical cases.Comment: 13 pages, 3 figures, minor changes are made to match the published
versio
Amplification of magnetic fields by dynamo action in Gaussian-correlated helical turbulence
We investigate the growth and structure of magnetic fields amplified by
kinematic dynamo action in turbulence with non-zero kinetic helicity. We assume
a simple Gaussian velocity correlation tensor, which allows us to consider very
large magnetic Reynolds numbers, up to one trillion. We use the kinematic
Kazantsev-Kraichnan model of dynamo and find a complete numerical solution for
the correlation functions of growing magnetic fields.Comment: 7 pages, 3 figure